Question

A radioactive material is known to decay at a yearly rate proportional to the amount at each moment. There were 1000 grams or the material 10 years ago. There are 980 grams right now. What will be the amount of the material right after 20 years? Select one: a. 10 ln^//ln (100/980)b. 10^6/980 c. 980^3/10^6 d. 980^2/10^3

Answer 1

Answer: c. 980^3/10^6

W1 = 980^3/10^6

The final amount after 20 years is 980^3/10^6 g

Explanation:

Given that the yearly decay is proportional to the amount at each moment.

W1 = K^n × (W) ....1

Where W1 is the final mass, W is the initial mass and K is the proportionality constant.

From equation 1

K^n = W1/W

For the ten years before now.

W = 1000

W1 = 980

We can now derive the value of K per 10 years

K(10) = 980/1000 per 10years

Since the current initial mass is 980

W = 980

K(10) = 980/1000 for 10 years.

In 20 years K(20) = K(10)^2

K(20) = (980/1000)^2

W1 = K(20) × W

W1 = (980/1000)^2 × 980

W1 = (980^3)/1000^2

W1 = 980^3/10^6

The final amount after 20 years is 980^3/10^6 g